Asked by Dino cat
Is (-2, 6) a solution to the system of these linear equations: x + 2y = 10 and 3x + y = 0? Why? (1 point)
No, because the graphs don't intersect at (-2, 6)
No, because the graphs intersect at (-2, 6)
Yes, because the graphs intersect at (-2, 6)
Yes, because the graphs don't intersect at (-2, 6)
No, because the graphs don't intersect at (-2, 6)
No, because the graphs intersect at (-2, 6)
Yes, because the graphs intersect at (-2, 6)
Yes, because the graphs don't intersect at (-2, 6)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine if the point (-2, 6) is a solution to the system of equations, we substitute x = -2 and y = 6 into both equations and check if they hold true.
1. For the first equation: \( x + 2y = 10 \)
\[
-2 + 2(6) = -2 + 12 = 10
\]
This is true.
2. For the second equation: \( 3x + y = 0 \)
\[
3(-2) + 6 = -6 + 6 = 0
\]
This is also true.
Since both equations are satisfied by the point (-2, 6), we conclude that this point is indeed a solution to the system of equations.
Therefore, the correct answer is:
**Yes, because the graphs intersect at (-2, 6).**
1. For the first equation: \( x + 2y = 10 \)
\[
-2 + 2(6) = -2 + 12 = 10
\]
This is true.
2. For the second equation: \( 3x + y = 0 \)
\[
3(-2) + 6 = -6 + 6 = 0
\]
This is also true.
Since both equations are satisfied by the point (-2, 6), we conclude that this point is indeed a solution to the system of equations.
Therefore, the correct answer is:
**Yes, because the graphs intersect at (-2, 6).**
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